The article introduces a tool called the fundamental theorem of asset pricing, which helps in pricing real-world assets by linking asset prices to states of the world and state prices. It explains how to identify arbitrage opportunities and apply them to option pricing. The concept of real-world and risk-neutral probabilities is discussed, showing that properly normalized asset prices have a Martingale property. The theorem helps in creating explicit stochastic differential equations for pricing and hedging. The article also covers binomial and trinomial trees for pricing and presents an application of the Martingale property. It concludes by discussing considerations for choosing pricing methods in practice.